Here is an example finger picking style to play to chords which I think sounds better than strumming.
G shown as an example. Repeat the style for each of the chords.
[Intro]
E|----------------------------------|
B|----0-----0-----0-----------------|
G|-------0-----0-----0-----0--------|
D|----------------------0-----------|
A|----------------------------------|
E|----3-----------------------------|
G G
Sleep tight tiger, sleep tight tiger
G C
Sleep tight tiger, sweet dreams till tomorrow
G
Sleep tight tiger
G G
Sleep tight tiger, sleep tight tiger
G C
I love you love you love you first thing in the morning
A Am
The day time the night time when the angels are calling
G C
They whisper they whisper in the top of my tongue
A Am
The tiny little words that tickles your ear drum
G G
Sleep tight tiger, sleep tight tiger
G C
Sleep tight tiger, sweet dreams till tomorrow
G
Sleep tight tiger
G C
Sleep tight tiger sweet dreams till tomorrow
A Am
I'll be teardrop in your pillow the beautiful sorrow
G C
I love you love you love you like I do in the noon
A Am
I am the shadow on your skin and I'll be gone very soon
G
Sleep tight tiger
G
Sleep tight tiger
G
Sleep tight tiger
G
Sleep tight tiger
A Am
I am the shadow on your skin and I'll be gone very soon
N.C.
The angels whisper
I am the shadow of your skin and I'll be gone tomorrow little tiger
Sleep tight little tiger
Sleep tight